with 20 subjects in a group and three groups, what f-ratio defines the 0.05 alpha level and what f-ratio defines the 0.01 alpha level

Question

this is for statistics analysis of variance, chi-square, correlatio

 

Answer 1

Hi, Kris!

 

Ok, so this is just asking for you to look up the critical F value associated with the 0.05 alpha level and the 0.01 alpha level.  Do answer this question, you'll need:

 

1) What an F ratio is.

2) What alpha is.

3) What a critical value is.

4) A textbook with an F table, or the internet.  

 

Let's get started.  I'm going to be brief for time's sake.

 

1) An F ratio is a ratio using two estimates of variance: one that will always be accurate (the denominator) and one that will only be accurate if the null hypothesis is true (the numerator).  You don't need to know much about calculating it to answer this question, though.  Just know that it is the result of you F test, or your Analysis of Variance (ANOVA).

 

2) Alpha is the probability that researchers are willing to accept that they might make what is called a "Type I" error, which I like to call an "Error of Overeagerness."  It's when we think we find something that's significant or true, but in reality, it's not.  It's like the fire alarm going off when there's no fire, or a pregnancy test that says your pregnant when you're not!  In the case of statistics, it generally means that you think your experiment worked when it really didn't.  We don't want this to happen, so we set in advance how frequently we're willing to let that happen (for a discussion of why we don't just always set it to zero, you'll have to write and ask!  It's too long to tell here!).  Two of the most accepted levels happen to be 0.05 and 0.01, or a 5% and 1% chance of a Type I error, respectively.

 

3) Critical values tell you what number your F ratio will be if the chances of getting a result as large or larger than the one you'll get through calculation if, in fact, the null hypothesis is true (e.g., what number is associated with that 0.05 and 0.01 Type I error rate, exactly?).

 

So.  To find this critical value, you need two kinds of degrees of freedom (df): between groups df and within groups df.  Between groups df is simply the number of groups in the study ("k") - 1.  So here we have 3 groups, so k - 1 = 2... df(between) =2.

 

Within groups df is the number of total people in the study ("N") - the number of groups ("k").  So here we have 60 people total (20 in each of 3 groups) and 3 groups.  So N - k = 60 - 3 = 57.  df(within) = 57.

 

Here's where you need the textbook or the internet.  To look up a critical value, you have to look across the table (left to right) using df(between).  So we'd go OVER 2 spaces.  Then you have look down the table (top to bottom) using df(within).  So we'd go down 57 spaces.  At that intersection, there should be two numbers: one for the 0.05 level, and one for the 0.01 level.  Let's see: this is a good one... http://vassarstats.net/textbook/apx_d.html

 

Going over 2 and down 57, we see 3.16 (at the 0.05 level) and 5.0 (at the 0.01 level).  Question answered!

 

Of course, really understanding what degrees of freedom, critical values, and F statistics really helps make sense of this... just let me know if you have a question I can answer!

 

Hope this helped!

 

Seth =)

 

 

20 subjects 3 groups